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Abstract

We extend the probability model for 3-layer radiative transfer [Opt. Express 20, 10004 (2012)] to ideal gas conditions where a correlation exists between transmission and temperature of each of the 3 layers. The effect on the probability density function for the at-sensor radiances is surprisingly small, and thus the added complexity of addressing the correlation can be avoided. The small overall effect is due to (a) small perturbations by the correlation on variance population parameters and (b) cancelation of perturbation terms that appear with opposite signs in the model moment expressions.

Figures (2)

The effect of within layer correlation on the pdf of the radiance for H0 (top), H1 (middle), and thermal contrast ΔT (bottom). Histograms from sampled data (dotted curves) and theoretical pdfs (solid curves) are shown. The figure shows that the pdfs computed in the presence of within-layer correlation,ρi=1, are very close to the pdfs in the absence of correlation, ρi=0. Theoretical pdfs and histograms are also very close to one another.